Measured data, such as the images generated by tomographic devices, are inherently imprecise . Previous, and a majority of current approaches, to visualization and analysis of structures have relied on modeling the structures precisely based, in one way or another, on ordinary (hard) set theory. The so called volume rendering processes recognized the need to somehow model the imprecision itself. While the philosophy underlying volume rendering seems very natural, it has not been pursued beyond just 3D structure visualization. Additionally, confining even to visualization, the intense computational and storage costs have made it difficult to pursue many important applications using volume rendering. Most importantly, it has not been possible to analyze structures in a quantifiable fashion, for example to measure and manipulate them, an ability which is increasingly being used in a variety of diagnostic therapeutic, and biomedical research applications. The specific aims of this research are to make interactive rendering, measurement, and manipulation of structures, all in the volume rendering paradigm, feasible. The approach consists of generalizing phenomena such as rendering, hidden-part removal, manipulation, and measurement that are based on ordinary sets to fuzzy sets. In the process, the efficiency of the algorithms that are based on ordinary sets are retained. The notion of a structure is imparted to volume rendering phenomenon through the notion of (fuzzily connected) fuzzy objects and fuzzy boundaries. A long-term goal of this research is to develop theory and algorithms for the analysis of multidimensional structures (e.g., cardiac motion and joint kinematics) from measured image sequences using the theory of fuzzy subsets. This seems to be a very sensible and useful direction to pursue.